# Small retrotetracontoctachoron

The **small retrotetracontoctachoron**, or **sirc**, is a nonconvex noble uniform polychoron that consists of 48 small rhombihexahedra. Eight cells join at each vertex.

Small retrotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sirc |

Elements | |

Cells | 48 small rhombihexahedra |

Faces | 288 squares, 144 octagons |

Edges | 576 |

Vertices | 144 |

Vertex figure | Square stephanoid, edge lengths √2 and √2+√2 |

Edge figure | sroh 4 sroh 8 sroh 4 sroh 8 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Dichoral angles | Sroh–8–sroh: 135° |

Sroh–4–sroh: 90° | |

Number of external pieces | 2736 |

Level of complexity | 40 |

Related polytopes | |

Army | Spic |

Regiment | Spic |

Conjugate | Great retrotetracontoctachoron |

Abstract & topological properties | |

Flag count | 9216 |

Euler characteristic | –48 |

Orientable | No |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | No |

Nature | Tame |

It can be constructed as a blend of 9 octagonal duoprisms, with the small rhombihexahedra being blends of 3 octagonal prisms. It can also be seen as the blend of 3 grand rhombic prismatotesseracts, each of which is a blend of 3 octagonal duoprisms.

## Vertex coordinates edit

Its vertices are the same as those of its regiment colonel, the small prismatotetracontoctachoron.

## External links edit

- Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#519).

- Klitzing, Richard. "sirc".

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